Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-05-02
AnnalsPhys.321:2491-2503,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, 1 figure, to appear in Annals of Physics
Scientific paper
10.1016/j.aop.2006.04.016
We study the classical and quantum cosmology of a 4+1-dimensional space-time with a non-zero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor $R(t)$ and an internal scale factor $a(t)$ associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that $a\sim R^{-1}$ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.
Jalalzadeh Shahram
Sepangi Hamid Reza
Vakili Babak
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